Blade fastening means

ABSTRACT

Blade fastening means are provided for securing airfoil blades around the periphery of a rotating member wherein the blades include contiguous stiffening or vibration dampening means which cooperate to form a shroud intermediate the ends of the blades. Each individual blade member may be removed or inserted without interference with the contiguous airfoil stiffening or vibration dampening means of the adjacent blade member and without the interposition of an individual spacer element between the blade root and groove.

United States Patent 1 Perkins 14 1 May 22, 1973 54] BLADE FASTENING MEANS 3,395,291 8/1968 Burge et al. ..4l6/220 3,572,970 3/1971 Smuland ..4l6/22l [75] Inventor: Alan Vincent Perkins, West 3,644,058 2/1972 Barnabei et al ..4l6/220 X Peabody, Mass. Primary Examiner-Everette A. Powell, Jr. Asslgneei General Elecmc Company Lynn Attorney Edward S. Roman, Derek P. Lawrence Massand Frank L. Neuhauser et al.

[21] Appl. No.: 222,847 Blade fastening means are provided for securing airfoil blades around the periphery of a rotating member wherein the blades include contiguous stiffening or [521 U.S. Cl ..4l6/220, 416/196 [51] Int. Cl ..F01d 5/32 brawn dampemng means wh'ch cooperate to form a 58 Field of Search ..416/219-22l 196 Shmud intermediate the ends blades- Each dividual blade member may be removed or inserted without interference with the contiguous airfoil stif- [56] References C'ted fening or vibration dampening means of the adjacent UNITED STATES PATENTS blade member and without the interposition of an individual spacer element between the blade root and 1 Morley et a1. groove 3,047,268 7/1962 Leavitt ....416/220 3,216,699 11/1965 Schoenbom ..4l6/220 X 6 Claims, 5 Drawing Figures Z 7! A A! l\ 7/ L Z ,5; 34 A /9 C A 7 Q 0 4 Z! in Z4 A7 *22 BLADE FASTENING MEANS The invention herein described was made in the course of or under a contract or subcontract thereunder with the Department of the Air Force.

BACKGROUND OF THE INVENTION In general, this invention relates to a blade fastening means for use in an axial flow turbomachine and more particularly to a blade fastening means which facilitates uninhibited insertion of individual blade elements within a shrouded blade assembly.

It is known that turbomachinery airfoils, for example, rotor blades and stator vanes used in steam or gas turbine components, including axial flow compressors and turbines, are subject to vibrations during operation. Frequently, with use of extremely long and thin blades or vanes, the vibrations can assume such proportions that dampening or stiffening of the airfoils is required. It is also known to use means projecting laterally of the airfoil portion of the blades or vanes and located intermediate or at the radial ends thereof for stiffening or dampening, these tongue-like projections conventionally interengaging like projections of adjacent airfoil members. Vibration dampening may thus be provided by frictional interengagement, as is disclosed in the U.S. Pat. No. 2,198,784 to Mikina. These integrally formed, laterally extending airfoil partitions may also be secured to each other at the lateral ends thereof for further stiffening of the row of blades or vanes. Thus as shown in the U.S. Pat. No. 2,472,886 to Conrad et al., provision may be made for blades having integral projections extending from opposite sides of the airfoil to be welded or lashed together to form a contiguous stiff ening ring or shroud member to avoid vibration or stress problems over the range of the turbomachine operating speeds.

Where it is desirable, however, that individual blades or vanes of a row be capable of being removed separately, when worn or damaged, it is inadvisable to permanently secure these lateral projections one to the other in the ring or shroud. Further, it has been found to be desirable for improved vibration dampening characteristics that the abutting edges of the opposing adjacent lateral airfoil partitions not be projected along lines parallel to the axial grooves or slots into which the blade or vane roots are inserted for support in the turbomachinery. Thus, contrary to the arrangement shown in the patent to Johansson U.S. Pat. No. 2,421,890, it is sometimes necessary that the joint formed by the abutting end portions of the intermediate blade partitions be projected along a line at an acute angle to the centerline of the blade retaining slots such that axially slidable removal of a single blade without interference between the lateral abutting projections of adjacent bladed members is impossible. An airfoil assembly as shown in-the patent to Schoenborn, U.S. Pat. No. 3,216,699 discloses an arrangement whereby airfoil members can be separately or individually removed and assembled in the retaining groove without interference between the contiguous, interengaging blade partitions of the stiffening or dampening means. However, in order to assemble or remove each individual blade, a spacer must also be assembled or removed axially in order that the blade may be moved radially within the groove permitting axial translation of the blade along the bottom surface of the groove without interference between the lateral partitions. The

blade spacer, however, increases the weight of the turbine assembly and provides an additional part which adds to the overall complexity of the turbine assembly.

Therefore, it is an object of this invention to provide a simplified and lightweight blade fastening means whereby airfoil members can be separately or individually removed and assembled in a retaining groove without interference between the contiguous interengaging blade partitions of a stiffening or dampening means.

It is also an object of this invention to provide a blade fastening means whereby airfoil members can be separately or individually removed and assembled in retaining grooves without interference between the contiguous interengaging blade partitions of a stiffening or dampening means and wherein the individual spacer elements conventionally disposed between the blade roots and the bottom surfaces of the grooves are eliminated.

SUMMARY OF THE INVENTION The blade fastening and locking means of this invention is provided for securing blades within an axial flow turbomachine assembly. The turbomachine assembly is of the type including a rotating member having a plurality of axial grooves disposed about the outer periphery thereof. The grooves extend axially through the rotating member and include opposing longitudinal sidewalls which diverge radially inward. A plurality of blade members having root and airfoil portions are provided for insertion within the grooves. The root portions are shaped to abut the groove sidewalls for retention within the grooves, there being clearance between the root portions and grooves to allow radial movement of the blades within the grooves. The blades further include stiffening means which project laterally from opposite surfaces of the airfoil portions. Opposing stiffening means contiguously form a shroud ring along lines of abutment directed at an angle to the axis of the grooves. A retaining ring means is fixedly attached to one of the radial surfaces of the rotating member and overlaps the open ended grooves to provide restraint against axial translation of the blade root portions in one direction. Flange means are provided which extend radially inward from the bottom surface of the blade root for engagement with the bottom wall of the groove so as to inhibit radial movement of the blade at one end of the root. The blade further includes a lip longitudinally extending from the other end of the blade root for engagement with the outer periphery of the retaining ring means to inhibit radial movement of the blade root at this end. Additional locking means are provided to restrain axial translation of the blade root portions in the opposing direction.

The clearance between the root portions and grooves is substantially equal to the radial extent of the shroud ring. The blade members may be individually translated a limited axial distance by slightly twisting the airfoil so as to allow engagement or disengagement of the radial flange and longitudinal lip with the bottom wall of the groove and the outer periphery of the retaining ringv DESCRIPTION OF THE DRAWINGS While the specification concludes with a series of claims which particularly point out and distinctly claim the invention described herein, it is believed that the invention will be more readily understood by reference to the discussion below and the accompanying drawings in which:

FIG. 1 is a cutaway perspective view of the blade fastening means of this invention;

FIG. 2 is a top view of the blade fastening means of FIG. 1;

FIG. 3 is a partial cross-sectional view of the blade fastening means of FIG. 1;

FIG. 4 is a partial cutaway perspective view of the blade fastening means of FIG. 1;

FIG. 5 is a partial cross-sectional view of an alternate embodiment of the blade fastening means of HG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT While an axial flow turbomachine compressor is depicted for illustrative purposes, it will be understood that the invention could equally be utilized in other turbomachinery components wherever it is desirable to stiffen or prevent vibration in rows of airfoil members by means of contiguous, frictionally engaged, lateral projections while at the same time permitting removal of individual blade or vane members which would otherwise be prevented by interference of the adjacent blade stiffening or vibration dampening means.

Indicated generally at in the drawings is a pair of identical rotor blades each having a radially extending airfoil portion 12. As best seen in FIGS. 3 and 4, the blade root or base portion includes pairs of oppositely directed, longitudinally extending faces and 16, end faces 17 and 18, and a bottom portion 19.

In the disclosed embodiment, the blade supporting structure comprises a rotor wheel disk, indicated generally at 22, having an enlarged rim portion 24 and a pair of oppositely directed (axially of the rotor) faces 26 and 28. Extending through the rim portion in a generally axial direction relative to the rotor are individual blade receiving grooves, indicated at 30, the best viewed in FIG. 4. These grooves comprise pairs of Iongitudinally extending angled sidewalls 32 and 33 and a wider base or bottom wall 34. As will be obvious from the drawings, the general overall shape of the disk or wheel grooves generally corresponds to the shape of the blade roots with a clearance between the bottom portion 19 of the blade roots and the base 34 of the grooves as indicated at A. Thus, longitudinal faces 15 and 16 of the blade roots are shaped to abut and be retained against action of centrifugal force by the angled walls 32 and 33 respectively, of the rotor wheel grooves 30.

As previously stated, it is often desirable, particularly with use of relatively long turbomachinery blading, to provide means for dampening vibrations through friction between members. The dampening or stiffening means may be integral with the blades, such as projections laterally of the blade airfoils and may be located intermediate or at the radially spaced airfoil ends. The blade lashings or partitions, as they are commonly called, may take the form of the contiguous, interengaging tongue-like elements, indicated generally at 40 and 42 in FIGS. 1 and 2. Each of these partition elements includes a bottom wall or surface 44, a top surface 46, and an end or lateral portion or wall 48. As shown, therefore, the partitions are generally flat, laterally extending members which, when in interengagement with adjacent members, form what may be termed a blade dampening ring or shroud.

During rotor operation the action of the motive fluid against the airfoils will cause the blades 10to untwist. This causes the abutting lateral wall portions 48 of partitions 40, 42 to rub; hence, dampening occurs by frictional vibration dampening. As seen in the plan view of FIG. 2, the ring or shroud is formed of the contiguous abutting partitions 40 and 42. It will be noted that the line of abutment coincides with the lateral portions 48 of adjacent partition elements and is angled or slanted with respect to the rotor grooves. This improves frictional dampening by causing increased rubbing during untwisting motion of the blades about their longitudinal axis during rotor operation. Also the plane of the abutting edges 48 of the adjacent partitions 40, 42 is in a generally radial direction with respect to the rotor axis.

FIG. 4 illustrates that the blade base groove 30 in the rotor disk extends between the opposed faces 26 28 of the disk in a generally axial direction, although they may be slightly angled to the axis of the turbomachine without departing from the intended scope of invention. Thus it will be apparent that movement axially longitudinally of the grooves will not permit the bladed members to be removed individually because of interference between the adjacent laterally extending partitions 40 42 of each blade of the row.

Means for locking the individual blades in the grooves to prevent axial separation from the disk will now be described. A circumferential, integral flange 50 projects radially inward from the underside of the forward portion of the wheel rim 24 and the forward face 52 of the flange 50 is made flush to face 26 of the rim 24. The root portion of each blade includes an integral lip 54, as best shown in FIGS. 3 and 4, which extends longitudinally outward from the outer radial portion of the end face 17 and wherein the forward edge of the lip may be radiused as shown in the drawings. The rim of the rotor wheel disk may also include corresponding integral lip sections 58 which extend longitudinally outward from the outer radial portion of the rim face 26. As is readily apparent from FIG. 4, when the individual blade elements are inserted within their respective grooves, the longitudinally extending lips 54 of the blade elements register with the longitudinally extending lip sections 58 of the wheel rim to form a completed annular lip.

Each blade root further includes an integral flange 60 as shown in FIG. 3 which extends radially inward from the aft end of the bottom portion 19 of the blade root. The length of the flange 60 is made equal to the clearance A between the bottom portion 19 of the blade root and the base 34 of the groove. The width of the flange 60 is also of critical dimension as will be made obvious from the following discussion.

An annular retaining ring shown generally at 62 is provided for restraining forward longitudinal motion of the blade roots within their respective grooves. One element of the retaining ring 62 includes a washer-type annulus 64 having opposed side faces 65 and 66 which extend in generally radial directions. The retaining ring 62 is affixed to the wheel 10 so that face 66 of the washer-type annulus abuts face 26 of the wheel rim 24 and face 52 of the flange 50. The retaining ring is maintained in affixed relationship to the wheel by a plurality of circumferentially spaced bolts 67 which extend through and clamp the washer-type annulus 64 to the radially inwardly directed flange 50. Attachment of the retaining ring could alternatively be achieved without the inwardly directed flange 50 by circumferentially disposing the bolt receiving holes intermediate the grooves 30.

Another element of the locking ring includes a flaired annulus 68 formed integral with the outer circumferential edge of the washer-type annulus 64. From the outer periphery of the flaired annulus there is provided an integral lip 70 extending in an outward radial direction. The outer periphery of the radial lip 70 is notched at 72 for engagement with the lips 54 of the blade roots and the lip sections 58 of the wheel rim. The notch 72 may be radiused to conform to the shape of the engaging lips of the blade roots and as is readily apparent from FIG. 3 the notch includes a portion 74 which supports the root lips 54 in an outward radial direction and a portion 73 which restrains the root lips from forward longitudinal translation. The portion 74 of the notch providing outward radial support to the root lips has an effective width designated generally at B wherein B is preferably equivalent to the width C of flange 60.

Longitudinal translation of the blade roots in the aft direction is restrained by means of a conventional snap ring 74 which is maintained in abutting relation to the faces 18 of the blade roots by overlapping hooks 75 which project from the face 28 of the wheel rim.

In assembling a row of airfoil members in an axial flow compressor or turbine, wherein the members have the vibration dampening or blade stiffening means described hereinabove, the steps of assembly may proceed as follows. Assuming the retaining ring 62 remains permanently affixed to the wheel rim after initial assembly, individual blades must be inserted into respective grooves from the aft side of the wheel. The individual blade members are slid into the respective grooves 30 with the bottom portion, or surfaces 19, of the blade roots resting on the bases or bottoms 34 of the grooves. Each blade is inserted all the way axially into the groove until the radial side of the flange 60 engages the face 28 of the wheel rim 24. The clearance A between the bottom portion 19 of the blade roots and the base 34 of the grooves is made substantially equal to the thickness of the partitions 40, 42, thus insuring that the contiguous partitions of adjacent blades do not interfere with the inserted blade when it is slid along the bottom portion of the wheel groove.

With the blade thus inserted, it must be raised and moved longitudinally forward only a limited distance equal to the width C of flange 60 or the width B of notch 72, whichever is greater, in order that the longitudinal faces and 16 of the blade root abut the oppositely directed sidewalls 32 and 33 of groove 30. The limited longitudinal translation of the blade necessary in order to engage the blade lip 54 within the notch 72 and to seat the inside edge of the flange 60 on the bottom portion of the wheel groove is made possible by the blade flexibility which permits a limited amount of airfoil twisting. Since the thickness of the lateral partition is substantially equal to the clearance A, the laterally extending dampening or stiffening partition means 40 and 42 of the blades now form the contiguous ring or shroud. Final restraint of the blades against translation in an aft direction is accomplished by insertion of the snap ring 74 within the overlapping hooks 75.

To remove an individual blade, the above described retention and assembly method is reversed. The snap ring 74 is first removed, whereupon a blade is then translated a limited distance in the aft direction by twisting the airfoil. The blade can then be dropped to the bottom surface of the wheel groove from where it can be entirely withdrawn from the groove without interference from the contiguous partitions of adjacent blades. lt should be understood that the designations of forward and aft are only presented by way of illustration and may be entirely reversed.

Referring to FIG. 5 where like numerals refer to previously described elements, there is shown a simplified alternate embodiment for the blade locking device of FIGS. 1 4. A simplified retaining ring 62' having opposed parallel sides 65', 66' has been substituted for the more complex retaining ring previously described. Retaining ring 62' is affixed to the wheel rim in identical manner utilizing circumferentially spaced bolts 67. As is apparent from FIG. 5, the circumferential notch 72 has been eliminated and forward axial translation of the blades 10 is prevented by engagement of face 66 with faces 17 of the blade roots. The longitudinal faces 15 and 16 of the blade roots are maintained in abutting relation with the oppositely directed sidewalls 32 and 33 of groove 30 by engagement of the outer periphery of the retaining ring 62' with the interior surfaces of the blade root lips 54 and by engagement of the bottom portions 34 of the wheel grooves 30 with the inside edges of the root flanges 60. As should be apparent from FIG. 5, insertion and withdrawal of the blades can be accomplished in the same manner as previously described.

While preferred embodiments of the present invention have been depicted and described, it will be understood that many modifications and changes may be made thereto without departing from the inventions fundamental theme.

Having thus described preferred embodiments of the invention, what is desired to be secured by letters patent is as follows:

1. Blade fastening and locking means for a turbomachine comprising:

a rotating member having a plurality of axial grooves disposed about the outer periphery thereof wherein the grooves include opposing sidewalls diverging radially inward;

a plurality of blade members having root and airfoil portions, the root portions being received in the grooves and shaped to abut the groove sidewalls for retention in the grooves, there being clearance between the root portions and grooves to allow radial movement therein;

a blade member stiffening means projecting laterally from the opposite surfaces of the airfoil portions, with opposing stiffening means contiguously forming a shroud ring along lines of abutment directed at an angle to the axis of the grooves;

a retaining ring means with an outer peripheral edge wherein the ring means is stationed in fixed relation relative to a radial surface of the rotating member so as to overlap one end of the grooves to provide restraint against axial translation of the blade root portions in one direction;

flange means extending radially inward from the bottom surface of the blade root for engagement with rotating member with a plurality of axial grooves disposed about the outer periphery thereof wherein the grooves include opposing sidewalls diverging radially inward; a plurality of blade members having root and airfoil portions, the root portions being received in the grooves and shaped to abut the groove sidewalls for retention in the grooves with clearance between the root portions and grooves to allow radial movement therein; and blade stiffening means projecting laterally from opthe bottom wall of the groove so as to inhibit radial movement of one end of the blade root;

lip means longitudinally extending from the other end of the blade root for engagement with the outer periphery of the retaining ring means to inhibit radial movement of the blade root at this end;

and locking means to provide restraint against axial translation of the blade root portions in the opposing direction wherein the clearance between the root portions and grooves is substantially equal to the radial extent of the shroud ring, and any one of the blade members may be translated a limited axial distance by slightly twisting the airfoil so as to allow engagement or disengagement of the radial flange and longitudinal lip with the bottom wall of the groove and the outer periphery of the retaining ring respectively, further permitting the blade members to be moved radially and removed from or inserted into their associated grooves individually and without interference from adjacent member stiffening means.

2. The blade fastening means of claim 1 wherein:

the rotating member includes a rotor wheel disk having an enlarged rim portion around the outer periphery thereof, through which the blade receiving grooves extend, and the outer periphery of the retaining ring is circumferentially notched for axial and radial engagement with the edge of the longitudinally extending lip means of each blade.

3. The blade fastening means of claim 2 wherein:

one side of the wheel rim includes an inwardly directed radial flange to which the retaining ring means is fixedly connected by means of a plurality of circumferentially spaced bolts extending therethrough and the locking means includes a snap ring for insertion within a plurality of circumferentially spaced hooks which extend from the radial surface of the wheel rim.

4. In an axial flow turbomachine assembly having a posite surfaces of the airfoil partitions, with opposing stiffening means contiguously forming a shroud ring along lines of abutment directed at an angle to the axis of the grooves wherein blade fastening and locking means comprise:

a retaining ring means with an outside peripheral edge wherein the ring is stationed in fixed relation relative to a radial surface of the rotating member so as to overlap one end of the grooves to provide restraint against axial translation of the blade root portions in one direction;

flange means extending radially inward from the bottom surface of each blade root for engagement with the bottom wall of the groove so as to inhibit radial movement of one end of the blade root, lip means longitudinally extending from the other end of the blade root for engagement with the outer periphery of the retaining ring to inhibit radial movement of the blade root at this end wherein any one of the blade members may be translated a limited axial distance by slightly twisting the airfoil so as to allow engagement or disengagement of the radial flange and longitudinal lip with the bottom wall of the groove and the outer periphery of the retaining ring means respectively further permitting the blade members to be moved radially and removed from or inserted into their associated grooves individually and without interference from adjacent member stiffening means.

5. The blade fastening means of claim 4 wherein:

the rotating member includes a rotor wheel disk having an enlarged rim portion around the outer periphery thereof, through which the blade receiving grooves extend, and the outer periphery of the retaining ring is circumferentially notched for axial and radial engagement with the edge of the longitudinally extending lip means of each blade.

6. The blade fastening means of claim 5 wherein:

one side of the wheel rim includes an inwardly directed radial flange to which the retaining ring means is fixedly connected by means of a plurality of circumferentially spaced bolts extending therethrough, and

the other side of the wheel rim includes a locking means to provide restraint against axial translation of the blade root portions in the opposing directlon. 

1. Blade fastening and locking means for a turbomachine comprising: a rotating member having a plurality of axial grooves disposed about the outer periphery thereof wherein the grooves include opposing sidewalls diverging radially inward; a plurality of blade members having root and airfoil portions, the root portions being received in the grooves and shaped to abut the groove sidewalls for retention in the grooves, there being clearance between the root portions and grooves to allow radial movement therein; a blade member stiffening means projecting laterally from the opposite surfaces of the airfoil portions, with opposing stiffening means contiguously forming a shroud ring along lines of abutment directed at an angle to the axis of the grooves; a retaining ring means with an outer peripheral edge wherein the ring means is stationed in fixed relation relative to a radial surface of the rotating member so as to overlap one end of the grooves to provide restraint against axial translation of the blade root portions in one direction; flange means extending radially inward from the bottom surface of the blade root for engagement with the bottom wall of the groove so as to inhibit radial movement of one end of the blade root; lip means longitudinally extending from the other end of the blade root for engagement with the outer periphery of the retaining ring means to inhibit radial movement of the blade root at this end; and locking means to provide restraint against axial translation of the blade root portions in the opposing direction wherein the clearance between the root portions and grooves is substantially equal to the radial extent of the shroud ring, and any one of the blade members may be translated a limited axial distance by slightly twisting the airfoil so as to allow engagement or disengagement of the radial flange and longitudinal lip with the bottom wall of the groove and the outer periphery of the retaining ring respectively, further permitting the blade members to be moved radially and removed from or inserted into their associated grooves individually and without interference from adjacent member stiffening means.
 2. The blade fastening means of claim 1 wherein: the rotating member includes a rotor wheel disk having an enlarged rim portion around the outer periphery thereof, through which the blade receiving grooves extend, and the outer periphery of the retaining ring is circumferentially notched for axial and radial engagement with the edge of the longitudinally extending lip means of each blade.
 3. The blade fastening means of claim 2 wherein: one side of the wheel rim includes an inwardly directed radial flange to which the retaining ring means is fixedly connected by means of a plurality of circumferentially spaced bolts extending therethrough and the locking means includes a snap ring for insertion within a plurality of circumferentially spaced hooks which extend from the radial surface of the wheel rim.
 4. In an axial flow turbomachine assembly having a rotating member with a plurality of axial grooves disposed about the outer periphery thereof wherein the grooves include opposing sidewalls diverging radially inward; a plurality of blade members having root and airfoil portions, the root portions being received in the grooves and shaped tO abut the groove sidewalls for retention in the grooves with clearance between the root portions and grooves to allow radial movement therein; and blade stiffening means projecting laterally from opposite surfaces of the airfoil partitions, with opposing stiffening means contiguously forming a shroud ring along lines of abutment directed at an angle to the axis of the grooves wherein blade fastening and locking means comprise: a retaining ring means with an outside peripheral edge wherein the ring is stationed in fixed relation relative to a radial surface of the rotating member so as to overlap one end of the grooves to provide restraint against axial translation of the blade root portions in one direction; flange means extending radially inward from the bottom surface of each blade root for engagement with the bottom wall of the groove so as to inhibit radial movement of one end of the blade root, lip means longitudinally extending from the other end of the blade root for engagement with the outer periphery of the retaining ring to inhibit radial movement of the blade root at this end wherein any one of the blade members may be translated a limited axial distance by slightly twisting the airfoil so as to allow engagement or disengagement of the radial flange and longitudinal lip with the bottom wall of the groove and the outer periphery of the retaining ring means respectively further permitting the blade members to be moved radially and removed from or inserted into their associated grooves individually and without interference from adjacent member stiffening means.
 5. The blade fastening means of claim 4 wherein: the rotating member includes a rotor wheel disk having an enlarged rim portion around the outer periphery thereof, through which the blade receiving grooves extend, and the outer periphery of the retaining ring is circumferentially notched for axial and radial engagement with the edge of the longitudinally extending lip means of each blade.
 6. The blade fastening means of claim 5 wherein: one side of the wheel rim includes an inwardly directed radial flange to which the retaining ring means is fixedly connected by means of a plurality of circumferentially spaced bolts extending therethrough, and the other side of the wheel rim includes a locking means to provide restraint against axial translation of the blade root portions in the opposing direction. 